Year: 2022
Author: Wolfgang Dahmen, Min Wang, Zhu Wang
Communications in Computational Physics, Vol. 32 (2022), Iss. 1 : pp. 1–40
Abstract
We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0217
Communications in Computational Physics, Vol. 32 (2022), Iss. 1 : pp. 1–40
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: State estimation in model-compliant norms deep neural networks sensor coordinates reduced bases ResNet structures network expansion.